The Question is from neet-physics , and it was created by the author P.NARASIMHA

Question

An electromagnetic wave has a frequency $f$ and wavelength $\lambda$ in a medium with refractive index $n$. If the same wave enters vacuum, which quantity remains unchanged?

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Properties of electromagnetic waves and refractive index.
 **Related Topics**: Wave speed, frequency, wavelength.
 **Prerequisites**: Understanding of wave properties, refractive index.
## SOLUTION PATHWAY
**Given Information**:
  * Frequency of the electromagnetic wave = $f$
  * Wavelength of the electromagnetic wave in the medium = $\lambda$
  * Refractive index of the medium = $n$
  * The wave enters vacuum.
**Method & Steps**:
 1. Relate wave speed, frequency, and wavelength.
  Reasoning: The speed of a wave ($v$) is related to its frequency ($f$) and wavelength ($\lambda$) by the equation $v = f\lambda$.
  Formula/Rule: $v = f\lambda$
 2. Consider the effect of the refractive index.
  Working: The refractive index ($n$) is the ratio of the speed of light in vacuum ($c$) to the speed of light in the medium ($v$): $n = \frac{c}{v}$.  Therefore, $v = \frac{c}{n}$.
  Key Point: The frequency of an electromagnetic wave remains constant when it passes from one medium to another. Only the speed and wavelength change.
 3. Determine the unchanged quantity.
  Result: When the wave enters vacuum ($n=1$), the speed becomes $v = c$, and the wavelength changes to $\lambda' = \frac{c}{f} = \frac{n\lambda}{1} = n\lambda$.  However, the frequency ($f$) remains constant.
  Verification:  The fundamental property of the wave (its frequency) is determined by the source and doesn't change when the wave enters a different medium.
 ## OPTION ANALYSIS
A ✓: Frequency remains unchanged. This is correct, as the frequency of the electromagnetic wave is an intrinsic property and does not depend on the medium.
B :x: Wavelength changes when the wave enters vacuum. The wavelength in vacuum will be $\lambda_{vacuum} = \frac{c}{f} = n\lambda$
C :x: Speed changes as the wave enters vacuum. Speed in vacuum is $c$, while in the medium it is $\frac{c}{n}$.
D :x: Neither wavelength nor speed remains unchanged.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Assuming that all wave properties change when the medium changes: Remember that frequency is an intrinsic property.
  2.Confusing refractive index with wavelength or speed: The refractive index is a ratio of speeds.
 **Quick Tips**:
  1.Remember the fundamental relationship $v = f\lambda$.
  2.Frequency is a source-dependent property and remains constant during medium changes.

P.NARASIMHA · Answer

The correct Option is "Frequency"

P.NARASIMHA · Answer

Wavelength

P.NARASIMHA · Answer

Speed

P.NARASIMHA · Answer

Both wavelength and speed

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